Programmers write programs that draw pictures and animate scenes on computer screens. To write these programs, programmers typically use mathematical formulations for computational geometry in two, three, and four dimensions. These mathematical formulations are highly specialized to a particular dimensionality. There is one formulation for two dimensions, another formulation for three dimensions, and yet another formulation for four dimensions. These formulations are based on conventions established during the last three centuries and have been baked into mathematics curricula for generations. Unfortunately, the formulations are error-prone when encoded in computer software and are not extensible to other dimensions.